Give simple verbal sentence for the following p: the lamp is off q: the room is dark. p rightarrow q ~(~p) ~p lambda ~q p doubleheadarrow q ~p v (~ p lambda q) ~(~ p lambda ~q) draw circuits for the following for 3 inputs a, b, c: not (a b) not (a + b) middot c for 2 inputs a, b: not (not a middot not b) + b for 3 inputs a, b, c: not ((not a middot b) + (not b c)) evaluate the circuit for following inputs a: true b:false c: true d false. a: true b:false c: true d false. a: true b:false c: true d false. a: true b:false c: true d false. a: true b:false c: true d false. give the logic expression for the above circuit use boolean rules and simplify a middot c + a middot d + b middot c + b middot d (c + a) (ab + abc) prove: (a + b)(a + b) = a